Pharmacodynamic analysis of time-variant cellular disposition: reticulocyte disposition changes in phlebotomized sheep

Abstract

Most pharmacodynamic (PD) models of cellular response assume a time-invariant (i.e., constant) cellular disposition despite known changes in the disposition with time, such as the reticulocyte residence time in the systemic circulation during stress erythropoiesis. To account for changes in cellular disposition, a comprehensive PD model that involves endogenous erythropoietin (Epo), reticulocytes, and hemoglobin responses was developed in phlebotomized sheep that considers a time-variant reticulocyte residence time and allows for the simultaneous determination of changes in the cellular disposition and cellular production. Five sheep were phlebotomized to hemoglobin concentrations of approximately 4 g/dl. Epo concentrations, reticulocytes, and hemoglobin concentrations were frequently sampled for 5-7 days prior to and 25-30 days following the phlebotomy. Initial steady-state conditions were assumed and the time-variant reticulocyte residence time in the systemic circulation was semiparametrically represented using a constrained spline function. Hemoglobin production was modeled using a Hill function via an effect site compartment. The initial steady state reticulocyte residence time in the systemic circulation was estimated as 0.477 (0.100) (mean (SD)) days, which maximally increased 2.01-to 2.64-fold higher than the initial steady-state residence time 5.95 (0.899) days post-phlebotomy (P < 0.01). On average, the residence time returned to steady-state values 15.4 (2.36) days post-phlebotomy, which was not significantly different from the initial steady-state value (P > 0.05). The baseline hemoglobin production rate was estimated at 0.0929 (0.0472) g/kg/day and the maximum production rate under stress phlebotomy was estimated at 0.504 (0.0422) g/kg/day. These data indicate that endogenously released Epo under acute anemic conditions can increase hemoglobin production approximately 5-fold. The determined increase in reticulocyte residence time produced under stress erythropoiesis is similar to the commonly reported 2-to 3-fold increase observed in human patients.

Erythropoietic Response to Endogenous Erythropoietin in Premature Very Low Birth Weight Infants

“…Therefore, as long as T Pk Ͻ t, k is the first phlebotomy after time t Ϫ L in vivo for the f prod total (t Ϫ b) term and the first phlebotomy after time t Ϫ T i for each Hb Ti ϫ f trans (t Ϫ T Ti ) term. The presented phlebotomy correction factor after l Ϫ k ϩ 1 phlebotomies is consistent with formulas previously derived after only one or two phlebotomies (Freise et al, 2007(Freise et al, , 2008.…”

“…The PD Hb mass balance model assumed that the behavior or disposition of the Hb and RBCs in the absence of phlebotomies was life span-based (i.e., based on removal of RBCs from the circulation through cellular aging/senescence) (Landaw, 1988;Krzyzanski et al, 2006;Freise et al, 2008). A time invariant "point distribution" (i.e., no variability) of RBC life spans was assumed (Krzyzanski et al, 2006;Freise et al, 2007). The Hb mass or amount in the infants was modeled as the summation of two separate components: 1) Hb contained in RBCs produced by the infant in vivo (Hb in vivo ) and 2) Hb contained in transfused RBCs (Hb trans ).…”

“…Hence, the time between production of progenitor cells and age-related death of RBCs, denoted by b, is given by b ϭ a ϩ L in vivo . Then, in the absence of any phlebotomies, the rate of change in the Hb amount that was produced in vivo is given by (Freise et al, 2007) …”

“…This is largely due to the complications in determining the erythropoiesis rate caused by frequent phlebotomies and RBC transfusions altering the RBC/Hb mass, and the effect of each phlebotomy on the RBC/Hb removal rate due to the life span-based disposition of RBCs (Landaw, 1988;Freise et al, 2007Freise et al, , 2008. Previous studies have demonstrated that on average 33.8 ml/kg blood is removed and 27.0 ml/kg blood is transfused during the first 4 weeks of life in infants born at a gestational age of less than 28 weeks (Madsen et al, 2000), and other studies have reported even higher phlebotomy blood loss volumes in the first 2 weeks of life alone (Lin et al, 2000;Widness et al, 2005).…”

Receptor-Based Dosing Optimization of Erythropoietin in Juvenile Sheep after Phlebotomy

“…These results seem to be similar to the results found in this study, although the variability in the lag time in this study was high. One publication has shown that under anemic conditions reticulocytes may be prematurely released into the bloodstream (Freise et al, 2007). Early release of reticulocytes will lead to earlier detection of new Hb in the bloodstream, which could contribute to study-to-study variability in lag time.…”